Wave Particle Duality Quantum Physics Lesson 3
Today’s Objectives • Explain what is meant by wave-particle duality. • Describe the main points of de Broglie’s hypothesis that matter particles also have a wave-like nature. • State and use the equation λ = h/p = h/mv • Describe evidence for de Broglie’s hypothesis.
Wave particle duality • We have seen…………….. Photons : Quanta (particles) of light Electrons: Being diffracted. A property of waves
Prince Louis de Broglie1892-1987 • Electrons should not be considered simply as particles, but that frequency must be assigned to them also. (1929, Nobel Prize Speech)
De Broglie (1924) • Suggested that particles such as electrons might show wave properties. • He summised that the de Broglie wavelength, λ was given by: m = mass v = velocity of the particle
Note that:- • This is a matter wave equation not electromagnetic wave • The de Broglie wavelength can be altered by changing the velocity of the particle.
Summary of Experiment • Beam of electrons directed at a thin metal foil. • Rows of atoms cause the electron beam to be diffracted in certain directions only. • We observe rings due to electrons being diffracted by the same amount from grains of different orientations, at the same angle to the incident beam.
Electron diffraction • 1927: Davisson & Gerner confirmed this prediction with experiments using electron beams. • They actually used a nickel target instead of a carbon one (we used) • The wavelength they measured agreed with de Broglie • There is a relationship between the accelerating voltage V and the k.e. of the particles
Diffraction effects have been shown for Hydrogen atoms Helium atoms Neutrons Neutron diffraction is an excellent way of studying crystal structures.
De Broglie Wavelength • In 1932, De Broglie discovered that all particles with momentum have an associated wavelength. What is the wavelength of a human being, assuming he/she weighs 70 kg, and is running at 25 m/s?
Practice Questions 1.Find the wavelength of an electron of mass 9.00 × 10-31 kg moving at 3.00 × 107 m s-1 2. Find the wavelength of a cricket ball of mass 0.15 kg moving at 30 m s-1. 3. It is also desirable to be able to calculate the wavelength associated with an electron when the accelerating voltage is known. There are 3 steps in the calculation. Calculate the wavelength of an electron accelerated through a potential difference of 10 kV.
Step 1: Kinetic energy EK = eV = 1.6 × 10-19 × 10000 = 1.6 × 10-15 J • Step 2: EK = ½ mv2 = ½m (mv) 2 = p2 / 2m, so momentum p = √2mEk = √2 × 9.1 × 10-31 × 1.6 × 10-15 = 5.4 × 10-23 kg m s-1 • Step 3: Wavelength λ = h / p = 6.63 × 10-34 / 5.4 × 10-23 = 1.2 × 10-11 m = 0.012 nm.
Slit spacing, d Wavelength, Distance to screen, L Fringe spacing, x d2 Laser d1 L1 Slits L2 Screen 1 Screen 2